338. Counting Bits

Given a non negative integer number num. For every numbers i in the range 0 ≤ i ≤ num calculate the number of 1's in their binary representation and return them as an array.

Example:
For num = 5 you should return [0,1,1,2,1,2].

Follow up:

• It is very easy to come up with a solution with run time O(n*sizeof(integer)). But can you do it in linear timeO(n) /possibly in a single pass?
• Space complexity should be O(n).
• Can you do it like a boss? Do it without using any builtin function like __builtin_popcount in c++ or in any other language.

class Solution {public:    vector<int> countBits(int num) {        vector<int> dp(1,0);        if(num>0) dp.push_back(1);        if(num<2) return dp;        int t=2;        while(t<=num)        {            int j=dp.size();            for(int i=0;i<j&&t<=num;++i,++t)            {                dp.push_back(1+dp[i]);                            }        }        return dp;    }};